DETERMINATION OF HEIGHTS BY BAROMETRIC METHODS. (AUK 
Of the former the Laplace formula is the most celebrated, and 
probably as reliable as any of the modifications suggested by 
subsequent authorities, whilst of the latter the one deduced by 
Professor Ferrel and set forth in the United States Coast and 
Geodetic Survey Report of 1881, may be taken as perhaps the 
most convenient and reliable. Reference may also be made to 
Lieut. Rennie’s paper in Trans. Royal Inst. Academy, vol. 23, 
part 2. The writer has taken many observations for the purpose 
of testing these formule against each other, and he generally 
finds that the “probable error ” as deduced by the method of 
least squares is about two-thirds as great with the Ferrel formula 
as with the Laplace. At the same time he finds that the Ferrel 
formula gives generally results about one-part in two hundred 
greater than those obtained from the Laplace one. This difference 
is caused by Ferrel using a slightly larger constant as the first 
term in his formula than Laplace (60,521°5 instead of 60,158°6). 
In cases where the writer has been able to check his results by 
actual “spirit levelling ” as practised by civil engineers, he has 
found his Laplace means nearer than his Ferrel ones. He therefore 
considers that the Ferrel formula with the Laplace constant 
restored would probably give the most accurate and consistent 
results. As the Ferrel formula is not often quoted by writers on 
barometric levelling the writer’s modification of it is given as an 
appendix to this paper. In reducing observations the barometric 
grade should always be ascertained and allowed for if possible. 
The writer always makes this correction in his work after a 
careful inspection of the isobaric charts prepared at the Melbourne 
Observatory for the period covered by his observations. 
The following series of heights deduced for a mountain, on one 
trip, will show what may be done. The observations were made 
with a siphon barometer, and at the time the writer considered 
the results decidedly inferior. The observations were taken on 
one day at hourly intervals. Computed heights, 2,068-°5 feet, 
2,070-1 ft., 2,078:2 ft., 2,081°9 ft., 2,090°8 ft. and 2,076°2 ft. 
Mean result, 2,077°6 ft. Max. differences from mean + 13:2 ft. 
and — 9:1 ft. 
As the result of the writer’s experience, it may be said that 
really reliable determinations of height (well within one per cent. 
of the truth, where the difference in height is considerable) may 
be made with mercurial barometers, that with the boiling-point 
apparatus an accuracy not very much inferior to that of the 
mercurial barometers can be attained, whilst with aneroids, if 
frequently checked, either with mercurials or the boiling-point 
apparatus, very valuable results may be obtained. Without such 
checks, however, they become unreliable. 
